It is known that when noise is present the measured correlation between two sets of data is incorrect, the degree of inaccuracy relating to the amount of noise. In order to reduce the amount of noise in data collection, such as in image collection in microscopy, it is known to extend the acquisition time, bin adjacent pixels or sum replicate images. Pixels in an image that are binned to form a new image, if a 1 to 4 binning is used the final image has only 25% of the original pixels.
FIG. 1 shows a diagram where it is shown that as the number of images that are averaged increases the measured correlation value r rises and approaches the known value 1.00. However the approach to the known value is asymptotic and it is difficult to acquire data of sufficient quality to accurately and precisely measure correlation.
When the data sets are images and the sources for instance are different channels in a microscope system, where each channel for instance uses light of different wavelengths, it is known to make correlation measurements in the form of colocalization measurements between the two source images. If there is any noise in such images, then a correlation or colocalization measurement will not fully recognise a perfect match between two images of the same specimen, even if two images collected from the same source and with the same specimen where used, a true match would not be recognised if there is some kind of noise or distortion in the collected data.
This is true for all sets of data where it is possible to acquire a replicate set of data, such that each entry in the replicate set of data is a second measurement of the same piece of data in the original data. Whenever there is noise in the process of collecting or acquiring the set of data or any other kind of distortion, the two images will never result in a perfect match in a correlation measurement.
It is also known that there are different ways of measuring the correlation between two sets of data. One known way is the Spearman rank correlation and another is the Pearson correlation. The accuracy of both of these known ways is dependent on the noise in the input data.